A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

To multiply terms with radicals, multiply the coefficients and radicands separately:

3\( \sqrt{9} \) x 8\( \sqrt{5} \)
(3 x 8)\( \sqrt{9 \times 5} \)
24\( \sqrt{45} \)

Now we need to simplify the radical:

24\( \sqrt{45} \)
24\( \sqrt{5 \times 9} \)
24\( \sqrt{5 \times 3^2} \)
(24)(3)\( \sqrt{5} \)
72\( \sqrt{5} \)

To subtract these radicals together their radicands must be the same:

5\( \sqrt{125} \) - 2\( \sqrt{5} \)
5\( \sqrt{25 \times 5} \) - 2\( \sqrt{5} \)
5\( \sqrt{5^2 \times 5} \) - 2\( \sqrt{5} \)
(5)(5)\( \sqrt{5} \) - 2\( \sqrt{5} \)
25\( \sqrt{5} \) - 2\( \sqrt{5} \)

Now that the radicands are identical, you can subtract them:

The equation for this sequence is:

a_n = a_n-1 + 4(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61

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